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Discussion of“The Puzzling Behavior of Sectoral Real
Exchange Rates”P. Kehoe and V. Midrigan
Franck Portier
Toulouse School of Economics
Hydra workshop 2012 – Ajaccio
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Three facts and an explanation
I Real exchange rates are volatile.
I Real exchange rates are persistent.
I Real exchange rates closely track nominal exchange rates.
I Nominal rigidities is a common explanation.
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Three facts and an explanation
“I mentioned recently that the correlation between nominal andreal exchange rates is one key piece of evidence that we live in aKeynes-Friedman world of sticky prices, not the classical, perfectflexibility world of real business cycle theorists”. Paul Krugman,February 5, 2011, NY Times Blog
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Pat and Virgiliu show:
I That the nominal rigidities story is indeed theoreticallypromising : stickier-priced goods tend to have more persistentreal exchange rates.
I But the story does not work quantitively: data on sectoral realexchange rate show that the degree of price rigidity does notmatter much for the three properties of RER.
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My discussion
I First I try to get some intuition in a static closed economymodel.
I Second, I comment on the quantitative part.
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1. Insights from a static closed economy model
I The RER is the ratio of the aggregate prices in the home andforeign countries
I Let me look at the relationship between price stickiness andrelative price movements in a closed economy
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1. Insights from a static closed economy model
I Preferences: log C − L + log(
MP
)I C =
(∫ 10 C
1−ρρ
i di
) ρρ−1
I Monopolistic firm i : Yi = `i
I Money supply M
I One period
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1. Insights from a static closed economy modelFlex price allocations
I From Hh FOC: PC = W and PC = Md , which gives inequilibrium (M = Md ): W = M
I Pricing: Pi = µW , with µ = ρρ−1
I Equilibrium:
P = µM
C =1
µ
I Money is neutral, Imperfect competition reduces output.
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1. Insights from a static closed economy modelFix price allocations
I Assume that firms set their prices in the morning.
I In the afternoon, before any production or trade, moneysupply unexpectedly changes, from M to γM
I Firms are not allowed to change their price, and must meetdemand.
I From Hh FOC, we still have: PC = W and PC = Md , whichgives in equilibrium (γM = Md ): W = γM
I P = µM is fixed
I Equilibrium output is given by PC = γM
P = µM
C =γ
µ
I Money is non-neutral, monetary expansion (γ > 1) isexpansionary.
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1. Insights from a static closed economy modelSticky price allocations
I Assume that firms set their prices in the morning.
I In the afternoon, before any production or trade, moneysupply unexpectedly changes, from M to γM
I Firms are allowed to change their price with probability 1 − λ,and if not must meet demand.
I If a firm can reset its price, Pflexi = µγM
I If not, Pfixi = µM
I Equilibrium:
P =((1 − λ)γ1−ρ + λ
) 11−ρ µM
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1. Insights from a static closed economy modelSticky price allocations
I I can compute the “persistence” of relative prices as thecorrelation between the relative price in the morning and therelative price in the afternoon, which is (obviously) increasingwith λ
I I can also compute the dispersion of relative price in theafternoon (cross-section) or the dispersion of price growthrates between morning and afternoon (time series)
I Let me do the time series:
I Morning: Pi = µM
I Afternoon: Pflexi = µγM with prob. 1 − λ and Pfix
i = µMwith prob. λ
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1. Insights from a static closed economy modelSticky price allocations
I Variance of growth factors:
λ(1 − λ)(γ − 1)2
I Comments:I start from flex price (λ = 0): increasing stickiness increases the
variance of relative prices growth,I The variance is increasing in γ (analogy with dynamic model
with accumulated shocks,I note that for λ > 1/2, the first effect is reversed (because only
one period)
I Insights:I “persistence” and dispersion of relative prices are magnified by
sticky prices with monetary shocksI Pat & Virgiliu show that these results go through for real
exchange rates in a two-country dynamic model
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2. Comments on the quantitative partData
I Impressive work on dataI For CPIs:
I 18 product categories, 1981-1995, EurostatI 66 product categories, 1996-2006, BLS
I Data on frequency of price adjustments:I Bils /Klenow for the USI Price data for Austria, Belgium, France, Spain
I Some work to much those different sources of information.
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2. Comments on the quantitative partStriking result of the small quantitative importance of price stickiness
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
year
qflex
(data)
qsticky
(data)
e
Figure 6A: Sectoral real exchange rates: most and least sticky sectors. Belgium.
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2. Comments on the quantitative partPersistence and stickiness
I The simple model predicts that the RER persistence is exactlythe λ parameter.
I This is clearly rejected by the data.
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2. Comments on the quantitative partPersistence and stickiness
0.2 0.4 0.6 0.8 10.7
0.75
0.8
0.85
0.9
0.95
1
1.05Belgium
0.2 0.4 0.6 0.8 10.7
0.75
0.8
0.85
0.9
0.95
1
1.05Austria
AR
(1)
co
eff
icie
nt
0.2 0.4 0.6 0.8 10.7
0.75
0.8
0.85
0.9
0.95
1
1.05France
O: 1- frequency of price changes
0.5 0.6 0.7 0.8 0.9 10.7
0.75
0.8
0.85
0.9
0.95
1
1.05Spain
OLS
Model
OLS
OLSOLS
Model
Model
Model
AR
(1)
co
eff
icie
nt
AR
(1)
co
eff
icie
nt
AR
(1)
co
eff
icie
nt
O: 1- frequency of price changes O: 1- frequency of price changes
O: 1- frequency of price changes
Figure 4: Stickiness vs. Real Exchange Rate Persistence: 1996-2006
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2. Comments on the quantitative partPersistence and stickiness
I But playing around with preferences, Pat & Virgiliu canobtain a flatter relation between ρ and λ.
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2. Comments on the quantitative partPersistence and stickiness
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 2: Persistence of relative prices and frequency of price changes: Separable preferences
U i: corr
(qi(s
t ),q
i(st-
1)
Oi: probability of not adjusting
V,G=1,0
V,G=5,5
V,G=1,1
V,G=1/5,1/5
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2. Comments on the quantitative partPersistence and stickiness
I Can we go further and get a flat relationship with a differentutility specification?
I Perhaps?
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2. Comments on the quantitative partThe λ ”parameter”
I λ is the probability of not adjusting.
I In the model, it is a parameter.
I But in the data, it is most likely an outcome (unless the Calvomodel is literally true).
I λ is not a deep parameter, but is affected by (among otherthings)
I Average inflation
US Austria Spain Belgium France
years covered 95-97 96-03 93-01 89-01 94-03
% CPI covered 69% 80% 70% 68% 65%
Include sales? Yes Yes No Yes Yes
Include return to a di§erent
regular price following a saleN/A N/A ? N/A N/A
Include price changes
due to product replacement?Yes Yes Yes No Yes
Include price changes
after stockout?Yes Yes ? Yes Yes
Include changes after
seasonal unavailability?Yes No ? No No
The statistics in all these datasets are available, in most cases, at a Öner level of
disaggregation than the Eurostat CPI data. We therefore aggregate these statistics (more on
this below) using those consumption expenditure weights used by the authors of the above-
mentioned studies. E.g., for US, these come from the 1995 CEX, for Spain these are the 1992
CPI weights, etc.
Aggregating statistics for 4-digit COICOP aggregates is straightforward for European
countries, where the narrower product categories correspond to a Öner COICOP disaggre-
gation (although, in some cases the COICOP classiÖcations di§er because of the di§erent
38
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2. Comments on the quantitative partThe λ ”parameter”
I λ is the probability of not adjusting.
I In the model, it is a parameter.
I But in the data, it is most likely an outcome (unless the Calvomodel is literally true).
I λ is not a deep parameter, but is affected by (among otherthings)
I Average inflationI Contractual environmentI Commercial regulation (for example on sales)I Dynamic competitive behaviors
I High lambdas could correspond to little nominal rigidities +stable environment.
I This would mess-up the analysis.
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